1

X-ray Beamline Design 1

X-ray Monochromator

Shunji GotoSPring-8/JASRI

September 25, 2012

Cheiron School 2012

2

Outline

1. Introduction2. Light source3. X-ray Monochromator

Fundamental of Bragg reflectionDynamical theoryDuMond diagram ~ extraction of x-rays from SRDouble crystal monochromatorCrystal cooling

4. Example of beamlines at SPring-85. Summary

33

SR

Experimental station

Exp. hallRing tunnel

Front-end

Beamline structureBeamline = “Bridge” between light source & experimental station

Transport and processing of photonsphoton energy, energy resolution,beam size, beam divergence, polarization,..

Light source

Monochromator, mirror

shutter, slit

pump,..

Vacuumprotection of ring vacuum and beamline vacuum

Radiation safety

Shielding and interlock

Bending magnet

Insertion device

Shielding hutch

Optics & transport

4

Light sources & X-ray optics

- White or monochromatic

- Energy range

- Energy resolution

- Flux & flux density

- Beam size at sample (micro beam?,...)

- Beam divergence/convergence at sample (Resolution in k-space)

- Higher order elimination w/ mirror

- Polarization conversion

- Spatial coherency

....

Check points to be considered for your SR application:

Light source, monochromator, mirror,

and other optical devices and components

5

BL classification (energy region)

Photon energy (eV)

IR

101 103 104 105

Undulator

Bending magnet

Wiggler

SX-PES

102

Earth,..HP/HT

Inelastic

Inelastic

SAXS

PX

XAFSPowder XRD

HP/HT XRD

NRS

SAXS

SX-MCD

PEEM

HX-PES

HXSXIR

100

Visible ~ UV~

6

BL classification (energy resolution)

Undulator

Bending magnet

White

Earth,..HP/HT

10-7 10-5 10-3

XAFSSAXS

XAFS

SAXS

PX

PX

Inelastic

NRSHX-PES

Topograph

Topograph

Surface ・interface XRF

Powder XRD

Wiggler Inelastic

Microbeam, imagingXMCD

Imaging

HP/HT XRD

Single crystal XRD

Energy resolution (ΔE/E)

7

Light sources (1)

Bending magnet or insertion devices ?

Bending magnet:for wide energy range, continuous spectrum

for wide beam application for large samples

Undulator (major part of 3GLS beamline):for high-brilliance beam

for micro-/ nano-focusing beam

Wiggler:for higher energy X-rays > 100 keV. 1012

1014

1016

1018

1020

1022

Bril

lianc

e (p

h/s/

mm

2/m

rad2

/0.1

% B

.W.)

100 101 102 103 104 105 106

Photon energy (eV)

Brilliance for SPring-8 casePower, brilliance, flux density, partial flux,.. can be calculated using code.

e.g. “SPECTRA” by T. Tanaka & H. Kitamura

8

Light sources (2)Angular divergence and band width

Core part we need

Bending magnet

Undulatorc

r λλ

γσ 1597.0≈′

nNK

N un

r21

21

2

2+=≈′ γλ

λσ

nNEE 1

≈Δ

SPring-8 in-vacuum undulator

9

γψ 1≈vPower distribution

consth ≈ψ

γψ 1≈vγψ Kh ≈

K: deflection parameter (K= 0.5~2.5)

]A[]rad[]m[]T[]GeV[27.1]kW[ 22tot IRBEP φ= ]A[]m[]T[21]GeV[27.1]kW[ 20

2tot ILBEP =

Total power

E= 8 GeV, I= 0.1 A, B= 0.68 T, R= 39.3 m Ptot= 0.15 kW/mrad

B0= 0.87 T, L= 4.5 mPtot= 14 kW

]m[ArcL ( )uzB λπ2sin220

Light sources (3)

Bending magnet Undulator

Kilowatt of SR power mostly eliminated before/by monochromator

10

X-ray MonochromatorX-ray monochromator is key component for SR experiments:

length gauge for structure analysis,energy gauge for spectroscopy,...

Principle of x-ray monochromator

Photon energy tuning Bragg’s law

Energy resolution source divergence, Darwin width,..

Flux (throughput) related to Darwin width

Understanding the dynamical theory for large & perfect crystal

Practical of the monochromator

Double-crystal monochromator for fixed-exit

Single-bounce monochromator is for limited case

Crystal cooling

High heat load depending on light source

Mechanical engineering issues

11

λθ md =Bsin2

θ θ d

dsinθ dsinθ

hKKQ =−= 0s

Bragg’s law in real space Laue condition (Kinematical)in reciprocal space

Reciprocal lattice vector h- Normal to net plane- Length = 1/d

1) Phase matching on the single net plane by mirror-reflection condition.

2) Phase matching between net planes.

net plane (spacing d)

Reciprocal lattice vector h

Scattering vector Q

Scattered wave Ks

Incident wave K0 θ θ

Bragg reflection

12

Ewald sphere

Ewald sphere:

When a reciprocal lattice point is on the Ewald sphere, Bragg reflection occurs.

Reciprocallattice points

0K

SK01 KRadius == λ

h

13

Top view

Side view

[100]

[011]

[010]

[001]

(400)

(511)

(111) : 3.1356 Ǻ(311) : 1.6375 Ǻ

(400) : 1.3578 Ǻ

(511) : 1.0452 Ǻ

a

a

d-spacing

(111) (311)

222 lkh

ad++

=

Miller indices and d-spacing for silicon

a = 5.431Å

Diamond : a = 3.567Å

14

( ) ( ) ( )∑ ⋅=j

jj iEfF rhhh π2exp,

( ) ( ) ( ){ }∑ ++=j

jjjj lzkyhxiEfF π2exp,hh

lkh ,, Mixture of odd and even numbers0=F

All odd, or, all even numbers, and m: integer,

mlkh 4=++ fF 8= 8 atoms in phase

14 ±=++ mlkh ( ) fiF ±= 14

24 ±=++ mlkh 0=F

Half contribute with phase shift ±π /2

lkh ,,

Half cancel with π

For diamond structure

Structure facrtor Sum of atomic scattering with phase shift in the unit cell

Position of atoms in the unit cell for diamond structure

(xj, yj, zj) =

(0, 0, 0)1, (1/4, 1/4, 1/4)2,

(1/2, 1/2, 0)3, (3/4, 3/4, 1/4)4,

(0, 1/2, 1/2)5, (1/4, 3/4, 3/4)6,

(1/2, 0, 1/2)7, (3/4, 1/4, 3/4)8

1

2zy

x

34

5

6

7 8Atomic scattering factor

Crystal structure factor for diamond structure

15

(400), (220),...

All in phase

[100]

[011]

(400)

(511)

a

(111) (311)

(111), (311),... Half contribute with phase shift ±π /2

(200)

(011), (200),...

Half cancel with π

Forbidden reflection

(011)

( ) fiF ±= 14fF 8=

0=F

Crystal structure factor for diamond structure

1616

X-ray monochromator using perfect crystal

Perfect single crystal: silicon, diamond,..

0

20

40

60

80

100

120

0 5 10 15 20 25 30Bragg angle (deg)

Pho

ton

ener

gy (k

eV)

Si 111 refl.

Si 311 refl.

Si 511 refl.

e.g. for SPring-8 standard DCM

Bragg angle: 3~27°

Photon energy tuning:

Crystal & lattice plane

Bragg angle range

Bsin][23984.12]keV[

θÅhkldE =

17

( ) ( ) 22 QQ GFII e ⋅=

Peak intensity 2xN

FWHM xx NNh 1~8858.0≈Δ

Crystal size becomes larger narrower & higher, approaching delta function

( ) ( )( )( )

( )( )

( )llN

kkN

hhNG zyx

ππ

ππ

ππ

2

2

2

2

2

22

sinsin

sinsin

sinsin

⋅⋅=QLaue function:

h, k, l: integer Intense peaks(hkl) reflection

3-dim. Periodic structure

0

20

40

60

80

100

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

120

( )( )h

hNxπ

π2

2

sinsin

h

One-dim. Laue function, Nx= 10

Kinematical X-ray diffraction

NxNy

Nz

cba zyx nnn ++

Unit cell

3-dimensional periodic structure of unit cell with number Nx, Ny, NzTotal scattering intensity becomes:

18

Dynamical theoryTwo-wave approximation

19

Kinematical to dynamical theory

“Large & perfect” single crystal:1) Multiple scattering w/ h & -h reflection2) Extinction

(Diffraction by “finite” number of net planes)

Kinematical diffraction is invalid Dynamical theory must be applied.

Net plane

Incident wave Diffracted wave

Extinction

20

Fundamental equation

h, g,... : Reciprocal lattice points

Eh, Eg : Fourier components of electric field

K0 : Incident wave vector in vacuum

kh : Wave vectors in the crystal

χh : Fourier components of the polarizability (Negative values, 10-6~10-5)

P= (eh・eg) : Polarization factor between h and g waves

kh= k0 + h : Momentum conservation

Fundamental equation is derived

using Maxwell’s equations and introducing Bloch wave

for 3-dimensional periodic medium (= perfect single crystal):

( )∑ ⋅=− −g

gghghhh EE

KKk eeχ2

0

20

2

21

Two-wave approximation

: Fourier components of the polarizability

(Negative values, 10-6~10-5)

: Polarization factor ( )

Fundamental equation is reduced to the equation for

two waves of incidence and “one” intense diffraction

( )∑ ⋅=− −g

gghghhh EE

KKk eeχ2

0

20

2 ( ) hhEPEEKKk

−+=− χχ 0002

0

20

20A

( ) hhhh EEPEKKk

002

22

B χχ +=−

hh −χχχ ,,0

( )hP ee ⋅= 0 BPP θπσ 2cos:,1: ==

22

Two-wave approximation

( ) hhEPEEKKk

−+=− χχ 0002

0

20

20A

( ) hhhh EEPEKKk

002

22

B χχ +=−

hE0χ

00Eχ

0Ehχ

Scheme of self-consistent wave field

hhE−χ0E⇒

hE⇒0E

hE

( )( ) 40222220 KPkk hhh −=−− χχkk( ) 2002 1 Kk χ+=

Using two equations, we obtain following secular equation:

h

h−

Secular equation

k : Mean wave number in the crystal

23

Boundary condition of wave vector

Tangential component of wave vector must be continuous.

Incident wave in vacuum

Refracted wave in the crystal

Bragg reflection in the crystal

Reflected wave in the crystal

Reflected wave in vacuum

K0 Kh

k0 kh

Vacuum Crystal

We must consider connections of waves from vacuum into the crystal and from the crystal to vacuum, to solve the equations.

24

Laue case and Bragg case

K0 Kh

n

K0 Kh

n

Laue case(Transmission geometry)

Bragg case(Reflection geometry)

25

Asymmetry ratio

h

bγγ 0=

nK ⋅= 00 ˆγ

nKhh ⋅= ˆγ

Laue case: b>0

Symmetric Laue case: b= 1

Bragg case: b< 0

Symmetric Bragg case: b= -1

K0 Kh

n

n: normal vector to the surface

26

Dispersion surface( )( ) 40222220 KPkk hhh −=−− χχkk

Two dispersion surfaces show the gap near Bragg condition.

h

kh

k0 O

H

Reciprocal spaceReal space

Secular equation is quartic equation, and it gives four-point solution on the n-vector,producing the dispersion surfaces.

n-Laue

n-Bragg

K0 Kh

n

K0 Kh

n

Laue case

Bragg case

0K

0K

Laue case

Bragg case

kh= k0 + h

27

Deviation from Bragg condition

Excitation errorGeometrical deviation ζ0 from Bragg condition:

Distance between Ewald sphere and the reciprocal lattice point.

ζ0 is positive when H is inside the Ewald sphere (by S. Miyake).

O

H

0K

SK 0ζ

h

( )0

20

0 22

Kh+⋅

−≈hKς

28

Normalized deviation parameter W

For symmetric Bragg case, sigma polarization:

Parameter W is related to the gap between two dispersion surfaces

and total reflection occurs at –1

29

Sign of deviation parameter W

Angle deviation at fixed energy

direction change of wave vector

Energy deviation at fixed angle

length change of wave vector

h h0W

00 →> WEE

0K0K

0EE =

30

Movement of tie point

(3) Higher angleW> 1

h

kh

k0 O

H

K0 Kh

Vacuum

Crystal

h

kh

k0 O

H

K0 Kh

Total reflection

(1) Lower angleW< -1

(2) Near Bragg condition-1< W< 1

h

kh

k0 O

H

K0 Kh

Dominant branch for thick Bragg-case crystal is close to O-sphere.

Tie point moves by changing the incident angle

at fixed photon energy (wavelength).

31

Calculation of polarizability

hihrh χχχ +=

For diamond structure

( ) Mc

ehr effv

r −′+−= 02

8π

λχ

M

c

ehi efv

r −′′−= 82

πλχ

( )fZv

r

c

er ′+−= 8

2

0 πλχ

fv

r

c

ei ′′−= 8

2

0 πλχ

mlkh 4=++

14 ±=++ mlkh

0=== lkh

( )( ) Mc

ehr effiv

r −′++−= 02

14π

λχ

( ) Mc

ehi efiv

r −′′+−= 142

πλχ

χh: Fourier component of polarizabilityproportional to the structure factor

vc: unit cell volume

( )EFv

r

c

eh ,

2

hπ

λχ −=

( ) ( )Effhr ′+⇔ h0χ

Atomic form factor + real part of anomalous factor

( )Efhi ′′⇔χImaginary part of anomalous factor

32

Amplitude ratio

From the solution of the fundamental equations, we obtain the ratio r = Eh/E0 ( reflection coefficient)as a function of parameter W.

For Bragg case, no absorption, and thick crystal:

( ) )1(1200

−−−−==−

WWWPP

EEr

h

hr

h

h

χχ

γγ

Total reflection

33

( ) )1(1 22 −−−= WWWR

hEEW

χχθθθ 1sin22sin 0B

2B ⎟

⎠⎞

⎜⎝⎛ +

Δ+Δ=

W: deviation parameter for s-polarization, symmetrical Bragg case

Angular deviation

Energy deviation

Geometry for symmetrical Bragg case

net plane

K0

Bθ SurfaceBθ

Khθθ Δ+Bθθ Δ+B

Refraction

Total reflection region

Darwin curve (intrinsic reflection curve for monochromatic plane wave)for Bragg case, no absorption, and thick crystal:

Reflectivity (Darwin curve)

34

Darwin curve

For Bragg case, no absorption, and thick crystal:

0

0.2

0.4

0.6

0.8

1

1.2

-5 -4 -3 -2 -1 0 1 2 3 4 5

W

Ref

lect

ivity

35

Reflectivity with absorption

- symmetrical Bragg case, - s-polarization, - thick crystal

12 −−= LLR

( ) ( )2

2222222

1

41

κ

κκ

+⎭⎬⎫

⎩⎨⎧ −++−−++

=gWgWgW

L

rh

hi

rh

igχχ

κχχ

== ,0hr

rEEW

χχθθθ 1sin22sin 0B

2B ⎟

⎠⎞

⎜⎝⎛ +

Δ+Δ=

Reflectivity

Note: No absorption curveDarwinRg →⇒== 0,0 κ

36

Reflectivity curve for silicon

・Width of 0.1～100 µrad・Peak ~1 with small absorption

回折幅

0

0.2

0.4

0.6

0.8

1

-100 -50 0 50 100Δθ (µrad)

Ref

lect

ivity

Si 111 refl. 10 keV

Si 333 refl. 30 keV

Examples for symmetrical Bragg case, with absorption, s-polarization and thick crystal:

Si 111 refl., 10 keV

( )( )i

i

i

r

i

r

+×−=

+×−=

×−=

×−=

−

−

−

−

11030.7

11066.3

1048.1

1078.9

8_111

6_111

70

60

χ

χ

χ

χ

( )( )i

i

i

r

i

r

+×−=

+×−=

×−=

×−=

−

−

−

−

11087.7

11024.2

1075.1

1007.1

10_333

7_333

90

60

χ

χ

χ

χ

Si 333 refl., 30 keV

37

Effective band width

2Darwin

2Bcot θθ Δ+Ω=

ΔEE

Energy resolution

B2sin θ

χhrEE

≈Δ

Angular width(Darwin width)

( )hFhr ∝=ΔB

Darwin 2sin2

θχ

θ

Gaussian approximation for both light source and reflection curve

EEΔRelative energy

1−=W 1=W

Incident angleBθ θ

Darwin width

Shift by refraction

Kinematical Bragg condition

Bcotθ−Slope:

EEΔRelative energy

Incident angle θ

Energy resolution

Effective band width

Light source divergence φ

Light source

ΔW= 2

The diagram helps to understand how we can extract x-rays from SR source.

DuMond (angle-energy) diagram

38

Source divergence and diffraction width

Divergence of undulator radiation ~ diffraction width

- Bending magnet

μrad60≈′rσ

- Undulator (N= 140)μrad5r ≈′σ

For SPring-8 case:

- Undulatorωλ

λγ

σh

11597.0 ∝≈′c

r

- Bending magnet

Natural divergence

ωλλσ

h

12

∝≈′u

r N

103

0 20 40 60 80 100

Photon energy (keV)

FWH

M (µ

rad)

102

101

100

10-1

Bending magnet

Undulator

Si 111 refl.

Si 311 refl.

Si 511 refl.

39

Energy resolution

For usual beamline : ΔE/E=10-5～10-3

22Bcot ωθ +Ω=

ΔEE Ω: source divergence,

ω: diffraction width

Angle-energy diagram(DuMond diagram)

φ

Pho

ton

ener

gy

Light source distribution

Δθ, φ

Acceptance by crystal

Resolution

10-5

10-4

10-3

10-2

0 20 40 60 80 100Photon energy (keV)

ΔE/E

BM & Si 111 refl.

BM & Si 311 refl.

BM & Si 511 refl.

Undulator & Si 111 refl.

40

DuMond diagram: undulator & DCMSPring-8 standard undulator

(λu= 32 mm, N= 140, K= 1.34, E1st= 10 keV)

+ DCM (Si 111 refl.)

10 keV (1st) 30 keV (3rd) 50 keV (5th)

Wider slit increases unused photons (power) on the monochromator !

Intensity distribution of

undulator

200

ΔE(e

V)

-50 500φ (μrad)

-200

0

600

ΔE(e

V)

-50 500φ (μrad)

-600

0

1000

ΔE(e

V)

-50 500φ (μrad)

-1000

0

φ

Acceptance by crystal

DE/

E= 2

x10-

4

50 μrad Undulator radiation: ( )2220 21 φγ++= KEE

41

DuMond diagram: undulator & DCM

SPring-8 standard undulator + 20 μrad slit + Si 111 DCM10-keV photons 1.3x10-4

100 μrad

ΔE/E

= 5x

10-4

-3

-2

-1

0

1

2

3

00.20.40.60.81Intensity (arb. units)

Rel

ativ

e en

ergy

(eV

)FWHM= 1.3 eV

Acceptance by Si 111 DCM

Undulator radiation

42

Improvement of energy resolution

(A) Collimation using slit (B) Collimation using pre-opticsw/ collimation mirror, CRL,..

(C) Additional crystalw/ (+,+) setting

(D) HR monochromator of π/2 reflection (~meV)

Pho

ton

ener

gy

Angle

ResolutionP

hoto

n en

ergy

Angle

Resolution

(B)~(D): restriction on photon energy

Pho

ton

ener

gy

Angle

Resolution

Light source distribution

Acceptance by crystal

Pho

ton

ener

gy

Angle

Resolution

Slit width

43

Improvement of energy resolution(C) Additional crystal w/ (+,+) setting

HXPES

Si 111 DCM Si nnn channel-cut mono.

Si 333 refl. for 6 keV

Si 555 refl. for 10 keV

40 μrad

ΔE/E

= 5x

10-5

-100

-80

-60

-40

-20

0

20

40

60

80

100

00.20.40.60.81

Intensity (arb. units)

Rel

ativ

e en

ergy

(meV

)

-100

-80

-60

-40

-20

0

20

40

60

80

100

00.20.40.60.81

Intensity (arb. units)

Rel

ativ

e en

ergy

(meV

)

FWHM= 45 meV

FWHM= 18 meV

Phot

on e

nerg

y

Angle

Resolution

44

Improvement of energy resolution

Si 111 DCM Si nnn back-scattering mono.

Si 999 refl. for 17.8 keV

Si 11 11 11 refl. for 21.7 keV

20 μrad

ΔE/E

= 5x

10-7

(D) HR monochromator of ~π/2 reflection (~meV) Inelastic scattering

Phot

on e

nerg

y

Angle

Resolution

-4

-3

-2

-1

0

1

2

3

4

00.20.40.60.81

Intensity (arb. units)

Rel

ativ

e en

ergy

(meV

)

-4

-3

-2

-1

0

1

2

3

4

00.20.40.60.81Intensity (arb. units)

Rel

ativ

e en

ergy

(meV

)

FWHM= 2.0 meV

FWHM= 0.87 meV

45

Photon flux after monochromatorPhoton flux (throughput) after monochromator can be estimated using effective band width:Photon flux (ph/s) =

Photon flux from light source (ph/s/0.1%bw)

x 1000

x Effective band width of monochromator

Throughput is estimated by overlapped area.

Note difference from energy resolution.

Pho

ton

ener

gy Light source

distribution

Angle

Effective band width

Acceptance by crystal

46

Effective band width

( ){ }λλχ fdf hklhr ′+∝ )(02

Independent of photon energy

Starting with Darwin width in the energy axis

)(02 hklhkl dfdEE

∝Δ

−=Δ

λλ

0

0.2

0.4

0.6

0.8

1

-5 -4 -3 -2 -1 0 1 2 3 4 5

10 keV30 keV

Ref

lect

ivity

2(x10-4)

1.4x10-4

ΔE/E

e.g. for Si 111 refl. DCM caseNote relative energy width is constant.

B2sin θ

χhrEE

≈Δ

Neglecting anomalous scattering factor f’

)(02 hklhr dfλχ ∝

22

B2

4

sin

λχ

θχ

λλ

hrhkl

hr

d

EE

=

≈Δ

−=Δ

47

Effective band width (Integrated intensity)

∫=Δ dWWREE hr 2

B2 )(sin2 θ

χ

0

2

4

6

8

10

12

14

0 20 40 60 80 100Photon energy (keV)

Effe

ctiv

e ba

nd w

idth

Si 111 refl.

Si 311 refl.

Si 511 refl., Si 333 refl.

(x10-5)

For double-crystal monochromator

When you need flux Lower order (Si 111 refl.,..)

When you need resolution Higher order (Si 311, Si 511 refl,..)

Effective band-width is obtained

by integration of reflection curve.

= ~2

48

Photon flux at undulator beamline

We can obtain photon flux of 1013~1014 ph/s/100 mA/mm2 using standard undulator sources and Si 111 reflections at SPring-8 beamlines.

1010

1011

1012

1013

1014

1015

1016

0 10 20 30 40 50Photon energy (keV)

Pho

ton

flux

(ph/

s/10

0 m

A) (a) total flux

(c)

(d)

(b) partial flux

(a) Total flux @ 0.1% b.w.(b) After frontend slit

1×1 mm2 @30 m(c) Si 111 refl. @10 keV

Effective b.w. = 1.3x10-4(d) 3rd harmonics @30 keV

Effective b.w. = 8.0x10-6

Higher harmonics elimination more mirror or detuning of DCM

49

Double-crystal monochromator

Fixed-exit operation for usability at experimental station.

Choose suitable mechanism for energy range(Bragg angle range).

Precision, stability, rigidity,...

Offset h

y θB

O

A B

z

1st crystal

2nd crystal

θBθB

Exit beam B

hyθsin2

AB ==

B

hzθcos2

OB ==

Fixed-exit operation using rotation (θ) + two translation mechanism

5050

e.g. Double-crystal monochromator

θ-stage

Translation stage

1st crystal

2nd crystal

θ-stage

y

h

SPring-8 BL15XU

KEK-PF BL-4CMatsushita et al., NIM A246 (1986)

θ stage

1st crystal2nd crystal

θ rotation centerY1 stage

Z-cam stage

SPring-8 std. DCMYabashi et al., Proc. SPIE 3773, 2 (1999)

θ1 + translation + θ2 computer link

θ + two translation (2 cams)

θ + two translation (1 cam)

h= 25 mm, θB= 5~70°Offset h= 30 mm

θB =3~27º for higher energy range

h= 100 mm,

θB= 5.7~72°(for lower energy range)

51

Crystal cooling

熱伝達

Qin T1

T0

Radiation & convection

Heat conduction in crystalHeat transfer

to coolant/holder Coolant/holder

Crystal

Why crystal cooling？Qin (Heat load by SR) = Qout (Cooling + Radiation,..)

with temperature rise ΔTαΔT = Δd (d-spacing change)

α: thermal expansion coefficientor Δθ (bump of lattice due to heat load)

Miss-matching between 1st and 2nd crystals occurs: Thermal drift, loss of intensity, broadening of beam, loss of brightnessMelting or limit of thermal strain Broken !

Solutions:(S-1) κ/α Larger(S-2) Contact area between crystal and coolant/holder

larger(S-3) Irradiation area Larger,

and power density smaller

Figure of meritSilicon Silicon Diamond300 K 80 K 300 K

κ (W/m/K) 150 1000 2000α (1/K) 2.5x10-6 -5x10-7 1x10-6

κ/α x106 60 2000 2000

We must consider:- Thermal expansion of crystal: α,- Thermal conductivity in crystal: κ,- Heat transfer to coolant and crystal holder.

Figure of merit of cooling:Good for silicon (80 k)

and diamond (300 K)

52

Crystal cooling at SPring-8

Linear undulator, N= 140, λu= 32 mm

Power & power density: 300~500 W , 300~500 W/mm2

a) Direct cooling of silicon pin-postcrystal – (S2) & (S3)

b) Silicon cryogenic cooling - (S1)

c) IIa diamond with indirect water cooling - (S1)

0.6 mm

0.6 mm

0.5 mm

0.2 mm

Water flow

Water flow

X-rays

O-ring

Si-Au-Si bonding

Power & power density:

~100 W, ~1 W/mm2

Fin crystal direct-cooling - (S2)

53

Example of x-ray beamline- SPring-8 case -

54

XAFS & single crystal diffraction

- Bending magnet- Collimator mirror, + DCM,+ refocusing mirror

Roller

ShaftLink

Motor

(a)

(b)

Bellows

x

yδ

Beamline center

Collimatormirror

Double-crystalmonochromator

Gammastopper

Downstreamshutter

G1-G3: Gear box

Refocusingmirror

J1-J6: Jack

Fixed point

Ideal reflection axis

(0, h)

(x0, y0)h-y0

J1 J2 J3 J4 J5 J6G1 G2 G3

5555

Protein crystallography

- Bending magnet- DCM + focusing mirror

Focusing mirror(Vertical deflection)

Double-crystalmonochromator

Shielded tube

Optics hutch with standard components

Experimental hutch

Distance from the source50 m30 m 40 m

56

High resolution inelastic scattering- Undulator- DCM + back-reflection monochromator & analyzer (w/ ~meV resolution)

Double-crystalmonochromator

Downstream shutter 1

Dual movableend-stopper

Experimental hutch 3(Back scattering hutch)

Experimental hutch 4(Analyzer hutch)

Experimentalhutch 2

Experimentalhutch 1

Optics hutch

Downstream shutter 2(Dual shutter)

Si 111 double-crystal beam displacerFocusing mirror

Downstream shutter 3 Back scattering

monochromator

Shielded beam ductSample position

Inclination stage

Distance from the source60 m30 m 40 m 50 m 70 m 80 m

5

57

200-m-long beamline

- Bending magnet- DCM

Biomedical imaging centerExperimental hutch 2 and 3

Distance from the source220 m200 m180 m160 m140 m120 m

120 m100 m80 m60 m40 m

Dry pump

Dry pump

Beam monitor andgate valve

Roots pump with dry pump

Arcade400-mm-diameter shielded beam duct

Front end

Experimental hutch 1

Storage ring building

Optics hutch with standard transport channel and optics

300-mm-wide beam at end-station

58

SummaryKey issues on the x-ray monochromator were shown,

introducing the dynamical x-ray diffraction for large & perfect crystal,

w/ several important points:

1) Total reflection occurs at the gap between dispersion surfaces.

2) Normalized deviation parameter W is related to the gap.

3) W is parameter of angular deviation and energy (wavelength) deviation.

It gives DuMond diagram as a band of |W|

59

Text books following Laue’s dynamical theory

Ergebnisse der Exakt Naturwiss.

10 (1931) 133-158.

R. W. James

“The Dynamical Theory of X-Ray Diffraction”

Solod State Physics 15, (1963) 53-220.

Dover (1945)

Oxford (2001)

B. W. Batterman & H. Cole

“Dynamical Diffraction of X-Rays by Perfect Crystals”

Rev. Modern Phys. 36,

(1964) 681-717.Springer (2004)

60

References

For monochromator[1] T. Matsushita & H. Hashizume,

Handbook on Synchrotron Radiation Vol. 1,

North-Holland (1983).

[2] Y. Shvyd’ko, Springer (2004), for high energy resolution

For atomic scattering factorFor f0

[3] International Tables for X-ray Crystallography (IUCr).[4] Hubbell et al.: J. Phys. Chem. Ref. Data Vol. 4, No. 3, 1975.For anomalous scattering factor f’, f”

[5] S. Sasaki, KEK report 88-14 (1989),[6] Tables of LBNL (B. L. Henke et al.),

http://henke.lbl.gov/optical_constants/index.html,[7] Tables of NIST,

http://physics.nist.gov/PhysRefData/FFast/html/form.htm

61

Thanks to:

H. Kitamura, T. Tanaka, S. Takahashi, K. Takeshita,

N. Nariyama, Y. Asano, H. Ohashi, T. Mochizuki,

M. Yabashi, H. Yamazaki, K. Tamasaku, A. Baron,

M. Suzuki, T. Uruga, T. Matsushita, T. Ohata,

Y. Furukawa, and T. Ishikawa

62

Thank you for your attention.